On model order priors for Bayesian identification of SISO linear systems

ABSTRACT

A method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.

KEYWORDS:

• System identification
• Bayesian estimation
• Metropolis Hastings sampler
• model order prior

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The phase of the estimates in Figures 1-2 is shifted by 2π to ease the comparison.

2. To ease the presentation, the phase of the estimates in Figures 5 and 6 is shifted by 6π and 2π respectively.

3. The PEM estimate is decomposed into the product of three rational functions to ease the presentation.

Additional information

Funding

This research was financially supported by the Swedish Foundation for Strategic Research (SSF) via the project ASSEMBLE and by the Swedish Research Council [grant number 2016-06079 (NewLEADS)], [grant number 621-2015-4393], [grant number 621-2013-5524], [grant number 621-2011-5890], [grant number 621-2009-4017].